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  • 1990-1994  (2)
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  • 1
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    Parameter Derivatives of the Jacobi Polynomials and the Gaussian Hypergeometric Function. (1994)
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    Publication Date: 2014-02-26
    Description: The paper's main result is a simple derivation rule for the Jacobi polynomials with respect to their parameters, i.e. for $\partial_{\alpha} P_n^{\alpha,\beta}$, and $\partial_{\beta} P_n^{\alpha,\beta}$. It is obtained via relations for the Gaussian hypergeometric function concerning parameter derivatives and integer shifts in the first two arguments. These have an interest on their own for further applications to continuous and discrete orthogonal polynomials. The study is motivated by a Galerkin method with moving weight, presents all proofs in detail, and terminates in a brief discussion of the generated polynomials.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
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    Moving Weight Galerkin Methods for Turbulent Reactive Flows (1994)
    Details
    Publication Date: 2014-02-26
    Description: Adopting a statistical approach for the computation of turbulent combustion flows an approximation for the probability density function (PDF) of the composition variables is often required to treat the highly non-linear reaction term in a satisfactory way. One class of methods currently being used are the moment methods which employ transport equations for low order statistical moments and use a parametrized shape of the PDF. A second class solves a transport equation for the joint PDF by a Monte Carlo method. In the present paper we develop an intermediate algorithm based on a Galerkin method for the PDF transport equation. The solution is developed in terms of an orthogonal or bi-orthogonal basis of a suitable Hilbert space. The unconventional use of the related weight function as a prefactor (moving weight approach) permits adaptivity and results in a generalization of the $\beta-$closure for bounded scalar quantities. We present the approximation procedure in detail and apply it to the evolution of the composition in a homogeneous well-stirred reactor. The extension to non-homogeneous flow simulations is straightforward.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
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